The goal of this work has been the theoretical analysis of dynamics from highly excited vibrational spectra of polyatomic molecules, especially, of molecules with classically chaotic dynamics. The excitation ranges of these spectra of highly excited molecules present fundamental new problems of spectral analysis which must first be overcome. We have sought to lay the foundation for a comprehensive new framework for analyzing spectra in which the dynamics are complicated by strongly interacting degrees of freedom. Ideally, this framework will allow for high energy unassignable spectra the kind of detailed level-by- level analysis customary at lower energy. To be really successful, we believe this scheme must be founded in a systematic understanding of the complex underlying classical dynamics of the molecule.